I think Henry's lightly testing Catherine to see if she approves of and/or shares his quirky sense of humor. By making fun of the standard get-to-know-you patter of Bath, Henry invites her to share a joke with him.

I think Catherine's lack of understanding is because she's inexperienced -- everything about Bath is new to her; she hasn't heard the standard pick-up lines enough to be able to make fun of them like Henry can. But to her credit, she seems to be trying her best to play along with Henry.